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POHow can you compare to what extent two lists are in the same order?
 

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    <p>I have two arrays containing the same elements, but in different orders, and I want to know the extent to which their orders differ.</p> <p>The method I tried, didn't work. it was as follows:</p> <p>For each list I built a matrix which recorded for each pair of elements whether they were above or below each other in the list. I then calculated a pearson correlation coefficient of these two matrices. This worked extremely badly. Here's a trivial example:</p> <pre> list 1: 1 2 3 4 list 2: 1 3 2 4 </pre> <p>The method I described above produced matrices like this (where 1 means the row number is higher than the column, and 0 vice-versa):</p> <pre> list 1: 1 2 3 4 1 1 1 1 2 1 1 3 1 4 list 2: 1 2 3 4 1 1 1 1 2 0 1 3 1 4 </pre> <p>Since the only difference is the order of elements 2 and 3, these should be deemed to be very similar. The Pearson Correlation Coefficient for those two matrices is 0, suggesting they are not correlated at all. I guess the problem is that what I'm looking for is not really a correlation coefficient, but some other kind of similarity measure. Edit distance, perhaps?</p> <p>Can anyone suggest anything better?</p>
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